Nonlinear impulsive system of fed batch in fermentation productive and its parameter identification

In this study the parameters identification problem of the fed batch glycerol fermentation process is investigated based on an impulsive dynamical system. Considering the abrupt increase of the glycerol and alkali in fed batch culture of glycerol by conversion to 1,3-propanediol, this paper proposes a nonlinear impulsive system of fed batch culture and its parameters identification problem. The existence and uniqueness of solution for the impulsive system and the continuous dependence of solution on the parameters are proved. Based on the compactness of the solution set of the system, identifiability of the system and the necessary condition of optimality for the system are obtained.